Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,2,Mod(577,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.577");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.i (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.70980888579\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 38) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.1 | ||
Root | \(-1.32288 + 2.29129i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.961 |
Dual form | 1216.2.i.k.577.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.32288 | + | 2.29129i | −0.763763 | + | 1.32288i | 0.177136 | + | 0.984186i | \(0.443317\pi\) |
−0.940898 | + | 0.338689i | \(0.890016\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.822876 | + | 1.42526i | −0.368001 | + | 0.637397i | −0.989253 | − | 0.146214i | \(-0.953291\pi\) |
0.621252 | + | 0.783611i | \(0.286624\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.64575 | −1.37796 | −0.688982 | − | 0.724778i | \(-0.741942\pi\) | ||||
−0.688982 | + | 0.724778i | \(0.741942\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.00000 | − | 3.46410i | −0.666667 | − | 1.15470i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.64575 | −1.40075 | −0.700373 | − | 0.713777i | \(-0.746983\pi\) | ||||
−0.700373 | + | 0.713777i | \(0.746983\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | + | 1.73205i | 0.277350 | + | 0.480384i | 0.970725 | − | 0.240192i | \(-0.0772105\pi\) |
−0.693375 | + | 0.720577i | \(0.743877\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.17712 | − | 3.77089i | −0.562131 | − | 0.973640i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.67712 | − | 4.02334i | 0.384759 | − | 0.923017i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.82288 | − | 8.35347i | 1.05244 | − | 1.82288i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.822876 | − | 1.42526i | −0.171581 | − | 0.297188i | 0.767391 | − | 0.641179i | \(-0.221554\pi\) |
−0.938973 | + | 0.343991i | \(0.888221\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.14575 | + | 1.98450i | 0.229150 | + | 0.396900i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.64575 | 0.509175 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.822876 | + | 1.42526i | 0.152804 | + | 0.264665i | 0.932257 | − | 0.361796i | \(-0.117836\pi\) |
−0.779453 | + | 0.626461i | \(0.784503\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.64575 | 1.01401 | 0.507003 | − | 0.861944i | \(-0.330753\pi\) | ||||
0.507003 | + | 0.861944i | \(0.330753\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.14575 | − | 10.6448i | 1.06984 | − | 1.85301i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.00000 | − | 5.19615i | 0.507093 | − | 0.878310i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.354249 | −0.0582381 | −0.0291191 | − | 0.999576i | \(-0.509270\pi\) | ||||
−0.0291191 | + | 0.999576i | \(0.509270\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.29150 | −0.847319 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.145751 | − | 0.252449i | 0.0227625 | − | 0.0394259i | −0.854420 | − | 0.519583i | \(-0.826087\pi\) |
0.877182 | + | 0.480158i | \(0.159421\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.64575 | + | 9.77873i | −0.860969 | + | 1.49124i | 0.0100257 | + | 0.999950i | \(0.496809\pi\) |
−0.870995 | + | 0.491292i | \(0.836525\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.58301 | 0.981336 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.17712 | + | 3.77089i | 0.317566 | + | 0.550041i | 0.979980 | − | 0.199098i | \(-0.0638011\pi\) |
−0.662413 | + | 0.749138i | \(0.730468\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.29150 | 0.898786 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.29150 | − | 10.8972i | −0.864204 | − | 1.49685i | −0.867835 | − | 0.496852i | \(-0.834489\pi\) |
0.00363070 | − | 0.999993i | \(-0.498844\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.82288 | − | 6.62141i | 0.515476 | − | 0.892831i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.00000 | + | 9.16515i | 0.927173 | + | 1.21395i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.96863 | − | 6.87386i | 0.516671 | − | 0.894901i | −0.483141 | − | 0.875542i | \(-0.660504\pi\) |
0.999813 | − | 0.0193585i | \(-0.00616237\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.468627 | + | 0.811686i | 0.0600015 | + | 0.103926i | 0.894466 | − | 0.447136i | \(-0.147556\pi\) |
−0.834464 | + | 0.551062i | \(0.814223\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.29150 | + | 12.6293i | 0.918643 | + | 1.59114i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.29150 | −0.408261 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.322876 | − | 0.559237i | −0.0394455 | − | 0.0683217i | 0.845629 | − | 0.533772i | \(-0.179226\pi\) |
−0.885074 | + | 0.465450i | \(0.845892\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.35425 | 0.524190 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.35425 | + | 2.34563i | −0.160720 | + | 0.278375i | −0.935127 | − | 0.354313i | \(-0.884715\pi\) |
0.774407 | + | 0.632687i | \(0.218048\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.854249 | + | 1.47960i | −0.0999822 | + | 0.173174i | −0.911677 | − | 0.410907i | \(-0.865212\pi\) |
0.811695 | + | 0.584082i | \(0.198545\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.06275 | −0.700066 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 16.9373 | 1.93018 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.00000 | + | 3.46410i | −0.225018 | + | 0.389742i | −0.956325 | − | 0.292306i | \(-0.905577\pi\) |
0.731307 | + | 0.682048i | \(0.238911\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.50000 | − | 4.33013i | 0.277778 | − | 0.481125i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.93725 | 0.871227 | 0.435613 | − | 0.900134i | \(-0.356531\pi\) | ||||
0.435613 | + | 0.900134i | \(0.356531\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.35425 | −0.466824 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.64575 | − | 6.31463i | −0.382179 | − | 0.661953i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.46863 | + | 12.9360i | −0.774461 | + | 1.34141i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.35425 | + | 5.70105i | 0.446736 | + | 0.584915i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.85425 | − | 3.21165i | 0.188270 | − | 0.326094i | −0.756403 | − | 0.654106i | \(-0.773045\pi\) |
0.944674 | + | 0.328012i | \(0.106379\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.29150 | + | 16.0934i | 0.933831 | + | 1.61744i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.82288 | − | 11.8176i | −0.678902 | − | 1.17589i | −0.975312 | − | 0.220831i | \(-0.929123\pi\) |
0.296411 | − | 0.955061i | \(-0.404210\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.2915 | 1.30965 | 0.654825 | − | 0.755780i | \(-0.272742\pi\) | ||||
0.654825 | + | 0.755780i | \(0.272742\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.93725 | + | 13.7477i | 0.774597 | + | 1.34164i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.2915 | 1.47829 | 0.739143 | − | 0.673549i | \(-0.235231\pi\) | ||||
0.739143 | + | 0.673549i | \(0.235231\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.29150 | − | 12.6293i | 0.698399 | − | 1.20966i | −0.270622 | − | 0.962686i | \(-0.587229\pi\) |
0.969021 | − | 0.246977i | \(-0.0794373\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.468627 | − | 0.811686i | 0.0444801 | − | 0.0770418i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.5830 | −1.46593 | −0.732963 | − | 0.680269i | \(-0.761863\pi\) | ||||
−0.732963 | + | 0.680269i | \(0.761863\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.70850 | 0.252569 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.00000 | − | 6.92820i | 0.369800 | − | 0.640513i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.5830 | 0.962091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.385622 | + | 0.667916i | 0.0347703 | + | 0.0602240i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.64575 | − | 11.5108i | −0.589715 | − | 1.02142i | −0.994270 | − | 0.106903i | \(-0.965907\pi\) |
0.404554 | − | 0.914514i | \(-0.367427\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −14.9373 | − | 25.8721i | −1.31515 | − | 2.27791i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.968627 | + | 1.67771i | −0.0846293 | + | 0.146582i | −0.905233 | − | 0.424915i | \(-0.860304\pi\) |
0.820604 | + | 0.571497i | \(0.193637\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.11438 | + | 14.6681i | −0.530184 | + | 1.27188i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.17712 | + | 3.77089i | −0.187377 | + | 0.324547i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.79150 | − | 13.4953i | −0.665673 | − | 1.15298i | −0.979102 | − | 0.203368i | \(-0.934811\pi\) |
0.313429 | − | 0.949612i | \(-0.398522\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.32288 | − | 16.1477i | −0.790756 | − | 1.36963i | −0.925499 | − | 0.378749i | \(-0.876354\pi\) |
0.134743 | − | 0.990881i | \(-0.456979\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.5203 | −0.970181 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.64575 | − | 8.04668i | −0.388497 | − | 0.672897i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.70850 | −0.224928 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.32288 | + | 14.4156i | −0.686459 | + | 1.18898i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.46863 | − | 9.47194i | 0.448007 | − | 0.775972i | −0.550249 | − | 0.835001i | \(-0.685467\pi\) |
0.998256 | + | 0.0590292i | \(0.0188005\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.9373 | −1.05282 | −0.526409 | − | 0.850231i | \(-0.676462\pi\) | ||||
−0.526409 | + | 0.850231i | \(0.676462\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.64575 | + | 8.04668i | −0.373156 | + | 0.646325i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.29150 | + | 9.16515i | −0.422308 | + | 0.731459i | −0.996165 | − | 0.0874969i | \(-0.972113\pi\) |
0.573857 | + | 0.818956i | \(0.305447\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 33.2915 | 2.64019 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.00000 | + | 5.19615i | 0.236433 | + | 0.409514i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.93725 | 0.308390 | 0.154195 | − | 0.988040i | \(-0.450722\pi\) | ||||
0.154195 | + | 0.988040i | \(0.450722\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.1144 | + | 17.5186i | 0.787403 | + | 1.36382i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.00000 | − | 10.3923i | −0.464294 | − | 0.804181i | 0.534875 | − | 0.844931i | \(-0.320359\pi\) |
−0.999169 | + | 0.0407502i | \(0.987025\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.50000 | − | 7.79423i | 0.346154 | − | 0.599556i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −17.2915 | + | 2.23695i | −1.32231 | + | 0.171064i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.00000 | + | 5.19615i | −0.228086 | + | 0.395056i | −0.957241 | − | 0.289292i | \(-0.906580\pi\) |
0.729155 | + | 0.684349i | \(0.239913\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.17712 | − | 7.23499i | −0.315761 | − | 0.546914i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.5000 | + | 18.1865i | 0.789228 | + | 1.36698i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.06275 | 0.303664 | 0.151832 | − | 0.988406i | \(-0.451483\pi\) | ||||
0.151832 | + | 0.988406i | \(0.451483\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.1144 | + | 19.2507i | 0.826125 | + | 1.43089i | 0.901056 | + | 0.433702i | \(0.142793\pi\) |
−0.0749311 | + | 0.997189i | \(0.523874\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.47974 | −0.183308 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.291503 | − | 0.504897i | 0.0214317 | − | 0.0371208i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.64575 | −0.701625 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.58301 | −0.476330 | −0.238165 | − | 0.971225i | \(-0.576546\pi\) | ||||
−0.238165 | + | 0.971225i | \(0.576546\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.29150 | + | 12.6293i | −0.524854 | + | 0.909074i | 0.474727 | + | 0.880133i | \(0.342547\pi\) |
−0.999581 | + | 0.0289406i | \(0.990787\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.35425 | − | 7.54178i | 0.311814 | − | 0.540078i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.64575 | 0.544737 | 0.272369 | − | 0.962193i | \(-0.412193\pi\) | ||||
0.272369 | + | 0.962193i | \(0.412193\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.93725 | − | 17.2118i | −0.704433 | − | 1.22011i | −0.966896 | − | 0.255172i | \(-0.917868\pi\) |
0.262462 | − | 0.964942i | \(-0.415465\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.70850 | 0.120508 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.00000 | − | 5.19615i | −0.210559 | − | 0.364698i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.239870 | + | 0.415468i | 0.0167533 | + | 0.0290175i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.29150 | + | 5.70105i | −0.228775 | + | 0.396250i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.79150 | + | 18.6914i | −0.538950 | + | 1.29291i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.64575 | − | 11.5108i | 0.457512 | − | 0.792435i | −0.541316 | − | 0.840819i | \(-0.682074\pi\) |
0.998829 | + | 0.0483843i | \(0.0154072\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.58301 | − | 6.20595i | −0.245503 | − | 0.425224i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.29150 | − | 16.0934i | −0.633675 | − | 1.09756i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.5830 | −1.39727 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.26013 | − | 3.91466i | −0.152725 | − | 0.264528i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.40588 | + | 16.2915i | −0.629864 | + | 1.09096i | 0.357714 | + | 0.933831i | \(0.383556\pi\) |
−0.987579 | + | 0.157126i | \(0.949777\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.58301 | − | 7.93800i | 0.305534 | − | 0.529200i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.35425 | −0.488119 | −0.244059 | − | 0.969760i | \(-0.578479\pi\) | ||||
−0.244059 | + | 0.969760i | \(0.578479\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.0000 | −1.32164 | −0.660819 | − | 0.750546i | \(-0.729791\pi\) | ||||
−0.660819 | + | 0.750546i | \(0.729791\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −22.4059 | + | 38.8081i | −1.47420 | + | 2.55339i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.43725 | + | 16.3458i | −0.618255 | + | 1.07085i | 0.371549 | + | 0.928413i | \(0.378827\pi\) |
−0.989804 | + | 0.142436i | \(0.954507\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.16601 | −0.467459 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.29150 | − | 9.16515i | −0.343720 | − | 0.595341i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.0000 | 0.776215 | 0.388108 | − | 0.921614i | \(-0.373129\pi\) | ||||
0.388108 | + | 0.921614i | \(0.373129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.79150 | + | 6.56708i | 0.244232 | + | 0.423022i | 0.961915 | − | 0.273347i | \(-0.0881308\pi\) |
−0.717683 | + | 0.696370i | \(0.754797\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.5830 | + | 18.3303i | 0.678900 | + | 1.17589i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.17712 | + | 8.96704i | −0.330754 | + | 0.572883i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.64575 | − | 1.11847i | 0.550116 | − | 0.0711668i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.5000 | + | 18.1865i | −0.665410 | + | 1.15252i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.6144 | − | 25.3128i | −0.922451 | − | 1.59773i | −0.795610 | − | 0.605810i | \(-0.792849\pi\) |
−0.126842 | − | 0.991923i | \(-0.540484\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.82288 | + | 6.62141i | 0.240342 | + | 0.416285i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.14575 | − | 10.6448i | −0.383361 | − | 0.664001i | 0.608179 | − | 0.793800i | \(-0.291900\pi\) |
−0.991540 | + | 0.129798i | \(0.958567\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.29150 | 0.0802501 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.29150 | − | 5.70105i | 0.203739 | − | 0.352886i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.46863 | + | 9.47194i | −0.337210 | + | 0.584065i | −0.983907 | − | 0.178682i | \(-0.942817\pi\) |
0.646697 | + | 0.762747i | \(0.276150\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 20.7085 | 1.27211 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.17712 | − | 10.6991i | 0.375234 | − | 0.649924i | −0.615128 | − | 0.788427i | \(-0.710896\pi\) |
0.990362 | + | 0.138503i | \(0.0442292\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 19.2915 | 1.16757 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.32288 | − | 9.21949i | −0.320981 | − | 0.555956i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 27.5203 | 1.65353 | 0.826766 | − | 0.562546i | \(-0.190178\pi\) | ||||
0.826766 | + | 0.562546i | \(0.190178\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −11.2915 | − | 19.5575i | −0.676005 | − | 1.17087i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.7288 | − | 22.0469i | −0.759334 | − | 1.31520i | −0.943191 | − | 0.332252i | \(-0.892192\pi\) |
0.183857 | − | 0.982953i | \(-0.441142\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.3229 | + | 26.5400i | −0.910850 | + | 1.57764i | −0.0979848 | + | 0.995188i | \(0.531240\pi\) |
−0.812866 | + | 0.582451i | \(0.802094\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −18.8229 | + | 2.43506i | −1.11497 | + | 0.144240i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.531373 | + | 0.920365i | −0.0313660 | + | 0.0543274i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.50000 | + | 14.7224i | 0.500000 | + | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.90588 | + | 8.49723i | 0.287588 | + | 0.498117i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −28.9373 | −1.69053 | −0.845266 | − | 0.534345i | \(-0.820558\pi\) | ||||
−0.845266 | + | 0.534345i | \(0.820558\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.53137 | + | 11.3127i | 0.380271 | + | 0.658649i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −12.2915 | −0.713225 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.64575 | − | 2.85052i | 0.0951763 | − | 0.164850i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.5830 | − | 35.6508i | 1.18638 | − | 2.05488i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 36.1033 | 2.07408 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.54249 | −0.0883225 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.322876 | + | 0.559237i | −0.0184275 | + | 0.0319173i | −0.875092 | − | 0.483956i | \(-0.839199\pi\) |
0.856665 | + | 0.515874i | \(0.172533\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.5830 | + | 30.4547i | −1.00026 | + | 1.73250i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.6458 | −0.773780 | −0.386890 | − | 0.922126i | \(-0.626451\pi\) | ||||
−0.386890 | + | 0.922126i | \(0.626451\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.43725 | − | 7.68555i | −0.250808 | − | 0.434413i | 0.712940 | − | 0.701225i | \(-0.247363\pi\) |
−0.963749 | + | 0.266812i | \(0.914030\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −24.0000 | −1.35225 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.00000 | − | 5.19615i | −0.168497 | − | 0.291845i | 0.769395 | − | 0.638774i | \(-0.220558\pi\) |
−0.937892 | + | 0.346929i | \(0.887225\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.82288 | − | 6.62141i | −0.214040 | − | 0.370728i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −20.2288 | + | 35.0372i | −1.12906 | + | 1.95559i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.29150 | + | 3.96900i | −0.127110 | + | 0.220160i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 19.2915 | + | 33.4139i | 1.06682 | + | 1.84779i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.93725 | − | 13.7477i | −0.437595 | − | 0.757937i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.8118 | 1.08895 | 0.544476 | − | 0.838776i | \(-0.316728\pi\) | ||||
0.544476 | + | 0.838776i | \(0.316728\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.708497 | + | 1.22715i | 0.0388254 | + | 0.0672476i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.06275 | 0.0580640 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.85425 | − | 8.40781i | 0.264428 | − | 0.458002i | −0.702986 | − | 0.711204i | \(-0.748150\pi\) |
0.967414 | + | 0.253202i | \(0.0814836\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 20.6144 | − | 35.7052i | 1.11962 | − | 1.93924i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −26.2288 | −1.42037 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.58301 | 0.139469 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.58301 | + | 6.20595i | −0.192903 | + | 0.334117i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.6144 | − | 20.1167i | 0.623492 | − | 1.07992i | −0.365338 | − | 0.930875i | \(-0.619047\pi\) |
0.988830 | − | 0.149046i | \(-0.0476201\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.1660 | −1.13299 | −0.566495 | − | 0.824065i | \(-0.691701\pi\) | ||||
−0.566495 | + | 0.824065i | \(0.691701\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.64575 | + | 4.58258i | 0.141220 | + | 0.244600i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.8745 | 0.685241 | 0.342620 | − | 0.939474i | \(-0.388686\pi\) | ||||
0.342620 | + | 0.939474i | \(0.388686\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.22876 | − | 3.86032i | −0.118290 | − | 0.204884i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.46863 | + | 4.27579i | −0.130289 | + | 0.225667i | −0.923788 | − | 0.382904i | \(-0.874924\pi\) |
0.793499 | + | 0.608572i | \(0.208257\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.3745 | − | 13.4953i | −0.703921 | − | 0.710278i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −14.0000 | + | 24.2487i | −0.734809 | + | 1.27273i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.40588 | − | 2.43506i | −0.0735872 | − | 0.127457i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.11438 | + | 14.0545i | 0.423567 | + | 0.733640i | 0.996285 | − | 0.0861125i | \(-0.0274444\pi\) |
−0.572718 | + | 0.819752i | \(0.694111\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.16601 | −0.0607001 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 22.9373 | + | 39.7285i | 1.19084 | + | 2.06260i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.00000 | 0.207112 | 0.103556 | − | 0.994624i | \(-0.466978\pi\) | ||||
0.103556 | + | 0.994624i | \(0.466978\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 15.8745 | − | 27.4955i | 0.819756 | − | 1.41986i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.64575 | + | 2.85052i | −0.0847605 | + | 0.146810i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.7085 | 0.550059 | 0.275029 | − | 0.961436i | \(-0.411312\pi\) | ||||
0.275029 | + | 0.961436i | \(0.411312\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 35.1660 | 1.80161 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.76013 | − | 4.78068i | 0.141036 | − | 0.244282i | −0.786851 | − | 0.617143i | \(-0.788290\pi\) |
0.927887 | + | 0.372861i | \(0.121623\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.9373 | + | 24.1400i | −0.710308 | + | 1.23029i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 45.1660 | 2.29592 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.00000 | + | 10.3923i | 0.304212 | + | 0.526911i | 0.977086 | − | 0.212847i | \(-0.0682735\pi\) |
−0.672874 | + | 0.739758i | \(0.734940\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.56275 | − | 4.43881i | −0.129273 | − | 0.223908i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.29150 | − | 5.70105i | −0.165613 | − | 0.286851i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.5314 | − | 18.2409i | 0.528554 | − | 0.915483i | −0.470891 | − | 0.882191i | \(-0.656068\pi\) |
0.999446 | − | 0.0332919i | \(-0.0105991\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −25.5203 | − | 33.4139i | −1.27761 | − | 1.67279i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.7915 | + | 23.8876i | −0.688715 | + | 1.19289i | 0.283539 | + | 0.958961i | \(0.408491\pi\) |
−0.972254 | + | 0.233928i | \(0.924842\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.64575 | + | 9.77873i | 0.281235 | + | 0.487113i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.11438 | + | 7.12631i | 0.204445 | + | 0.354109i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.64575 | 0.0815769 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.79150 | + | 6.56708i | 0.187478 | + | 0.324721i | 0.944409 | − | 0.328774i | \(-0.106635\pi\) |
−0.756931 | + | 0.653495i | \(0.773302\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 41.2288 | 2.03366 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −14.4686 | + | 25.0604i | −0.711955 | + | 1.23314i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.53137 | + | 11.3127i | −0.320612 | + | 0.555317i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 49.3320 | 2.41580 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −31.7490 | −1.55104 | −0.775520 | − | 0.631322i | \(-0.782512\pi\) | ||||
−0.775520 | + | 0.631322i | \(0.782512\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.4059 | + | 21.4876i | −0.604626 | + | 1.04724i | 0.387485 | + | 0.921876i | \(0.373344\pi\) |
−0.992111 | + | 0.125366i | \(0.959989\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.70850 | − | 15.0836i | 0.423422 | − | 0.733388i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.70850 | − | 2.95920i | −0.0826800 | − | 0.143206i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 24.5830 | 1.18688 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.9373 | + | 24.1400i | 0.671334 | + | 1.16278i | 0.977526 | + | 0.210815i | \(0.0676117\pi\) |
−0.306192 | + | 0.951970i | \(0.599055\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.93725 | − | 15.4798i | −0.429497 | − | 0.743911i | 0.567332 | − | 0.823489i | \(-0.307976\pi\) |
−0.996829 | + | 0.0795788i | \(0.974642\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.58301 | − | 6.20595i | 0.171792 | − | 0.297552i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.11438 | + | 0.920365i | −0.340327 | + | 0.0440270i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.40588 | − | 9.36326i | 0.258009 | − | 0.446884i | −0.707700 | − | 0.706513i | \(-0.750267\pi\) |
0.965708 | + | 0.259629i | \(0.0836004\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.5830 | − | 21.7944i | −0.599191 | − | 1.03783i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.32288 | − | 9.21949i | −0.252897 | − | 0.438031i | 0.711425 | − | 0.702762i | \(-0.248050\pi\) |
−0.964322 | + | 0.264731i | \(0.914717\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.4686 | + | 25.0604i | 0.684343 | + | 1.18532i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.2915 | −1.14639 | −0.573193 | − | 0.819420i | \(-0.694296\pi\) | ||||
−0.573193 | + | 0.819420i | \(0.694296\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.677124 | + | 1.17281i | −0.0318845 | + | 0.0552256i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 17.1144 | − | 29.6430i | 0.804104 | − | 1.39275i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12.0000 | 0.562569 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.8745 | 1.53780 | 0.768902 | − | 0.639366i | \(-0.220803\pi\) | ||||
0.768902 | + | 0.639366i | \(0.220803\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.58301 | − | 16.5983i | 0.446325 | − | 0.773058i | −0.551818 | − | 0.833964i | \(-0.686066\pi\) |
0.998143 | + | 0.0609066i | \(0.0193992\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 38.4575 | 1.78727 | 0.893636 | − | 0.448792i | \(-0.148146\pi\) | ||||
0.893636 | + | 0.448792i | \(0.148146\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −12.2915 | − | 21.2895i | −0.570005 | − | 0.987277i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.3542 | −0.895608 | −0.447804 | − | 0.894132i | \(-0.647794\pi\) | ||||
−0.447804 | + | 0.894132i | \(0.647794\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.17712 | + | 2.03884i | 0.0543546 | + | 0.0941448i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.0000 | − | 24.2487i | −0.645086 | − | 1.11732i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 26.2288 | − | 45.4295i | 1.20600 | − | 2.08885i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.90588 | − | 1.28149i | 0.454513 | − | 0.0587989i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −25.1660 | + | 43.5888i | −1.15227 | + | 1.99579i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.29150 | + | 5.70105i | 0.150393 | + | 0.260488i | 0.931372 | − | 0.364069i | \(-0.118613\pi\) |
−0.780979 | + | 0.624557i | \(0.785280\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.354249 | − | 0.613577i | −0.0161523 | − | 0.0279767i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −15.8745 | −0.722315 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.05163 | + | 5.28558i | 0.138567 | + | 0.240006i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.22876 | −0.191623 | −0.0958116 | − | 0.995399i | \(-0.530545\pi\) | ||||
−0.0958116 | + | 0.995399i | \(0.530545\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.20850 | + | 9.02138i | −0.235536 | + | 0.407961i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.6458 | + | 34.0274i | −0.886600 | + | 1.53564i | −0.0427320 | + | 0.999087i | \(0.513606\pi\) |
−0.843868 | + | 0.536550i | \(0.819727\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −30.5830 | −1.37460 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.93725 | − | 8.55157i | 0.221466 | − | 0.383591i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.38562 | − | 4.13202i | 0.106795 | − | 0.184975i | −0.807675 | − | 0.589628i | \(-0.799274\pi\) |
0.914470 | + | 0.404653i | \(0.132608\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 31.7490 | 1.41844 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.4686 | − | 35.4527i | −0.912651 | − | 1.58076i | −0.810305 | − | 0.586009i | \(-0.800698\pi\) |
−0.102346 | − | 0.994749i | \(-0.532635\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.4575 | 0.999346 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.9059 | + | 20.6216i | 0.528759 | + | 0.915837i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.8745 | − | 27.4955i | −0.703625 | − | 1.21871i | −0.967185 | − | 0.254072i | \(-0.918230\pi\) |
0.263560 | − | 0.964643i | \(-0.415103\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.11438 | − | 5.39426i | 0.137772 | − | 0.238628i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.43725 | − | 10.6448i | 0.195910 | − | 0.469977i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.9373 | + | 18.9439i | −0.481953 | + | 0.834767i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.1144 | − | 17.5186i | −0.444830 | − | 0.770468i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.93725 | − | 13.7477i | −0.348407 | − | 0.603458i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.7085 | −0.512959 | −0.256479 | − | 0.966550i | \(-0.582563\pi\) | ||||
−0.256479 | + | 0.966550i | \(0.582563\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.937254 | + | 1.62337i | 0.0409833 | + | 0.0709851i | 0.885789 | − | 0.464087i | \(-0.153618\pi\) |
−0.844806 | + | 0.535072i | \(0.820284\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 22.1033 | 0.964666 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.1458 | − | 17.5730i | 0.441120 | − | 0.764042i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −31.7490 | −1.37779 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.583005 | 0.0252528 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.5830 | + | 21.7944i | −0.544011 | + | 0.942254i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.37451 | + | 9.30892i | −0.231927 | + | 0.401710i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −29.2288 | −1.25897 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.00000 | + | 6.92820i | 0.171973 | + | 0.297867i | 0.939110 | − | 0.343617i | \(-0.111652\pi\) |
−0.767136 | + | 0.641484i | \(0.778319\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −58.8118 | −2.52385 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.0000 | + | 20.7846i | 0.514024 | + | 0.890315i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.64575 | − | 9.77873i | −0.241395 | − | 0.418108i | 0.719717 | − | 0.694268i | \(-0.244272\pi\) |
−0.961112 | + | 0.276159i | \(0.910938\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.87451 | − | 3.24674i | 0.0800020 | − | 0.138568i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.11438 | − | 0.920365i | 0.303083 | − | 0.0392089i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.29150 | − | 12.6293i | 0.310066 | − | 0.537050i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.771243 | + | 1.33583i | 0.0327375 | + | 0.0567029i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.70850 | − | 4.69126i | −0.114763 | − | 0.198775i | 0.802922 | − | 0.596084i | \(-0.203277\pi\) |
−0.917685 | + | 0.397309i | \(0.869944\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22.5830 | −0.955159 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.0627 | 0.424094 | 0.212047 | − | 0.977259i | \(-0.431987\pi\) | ||||
0.212047 | + | 0.977259i | \(0.431987\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.8229 | − | 22.2099i | 0.539462 | − | 0.934376i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.11438 | + | 15.7866i | −0.382768 | + | 0.662973i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.58301 | 0.275974 | 0.137987 | − | 0.990434i | \(-0.455937\pi\) | ||||
0.137987 | + | 0.990434i | \(0.455937\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.81176 | 0.326912 | 0.163456 | − | 0.986551i | \(-0.447736\pi\) | ||||
0.163456 | + | 0.986551i | \(0.447736\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.70850 | − | 15.0836i | 0.363803 | − | 0.630125i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.88562 | − | 3.26599i | 0.0786359 | − | 0.136201i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.0000 | 0.457936 | 0.228968 | − | 0.973434i | \(-0.426465\pi\) | ||||
0.228968 | + | 0.973434i | \(0.426465\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −19.2915 | − | 33.4139i | −0.801727 | − | 1.38863i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −28.9373 | −1.20052 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 29.2288 | + | 50.6257i | 1.21053 | + | 2.09670i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.58301 | + | 11.4021i | 0.272174 | + | 0.471419i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.06275 | − | 12.2330i | 0.291511 | − | 0.504911i | −0.682656 | − | 0.730739i | \(-0.739175\pi\) |
0.974167 | + | 0.225828i | \(0.0725088\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.46863 | − | 22.7148i | 0.390148 | − | 0.935946i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.1144 | + | 17.5186i | −0.416050 | + | 0.720620i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.8542 | − | 25.7283i | −0.609991 | − | 1.05654i | −0.991241 | − | 0.132063i | \(-0.957840\pi\) |
0.381250 | − | 0.924472i | \(-0.375494\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 52.5830 | 2.15208 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.46863 | − | 14.6681i | −0.346019 | − | 0.599322i | 0.639520 | − | 0.768775i | \(-0.279133\pi\) |
−0.985538 | + | 0.169453i | \(0.945800\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.4170 | 0.424918 | 0.212459 | − | 0.977170i | \(-0.431853\pi\) | ||||
0.212459 | + | 0.977170i | \(0.431853\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.29150 | + | 2.23695i | −0.0525941 | + | 0.0910956i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.70850 | + | 15.0836i | −0.354051 | + | 0.613234i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.93725 | −0.281574 | −0.140787 | − | 0.990040i | \(-0.544963\pi\) | ||||
−0.140787 | + | 0.990040i | \(0.544963\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 15.8745 | 0.643268 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.35425 | + | 7.54178i | −0.176154 | + | 0.305108i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.70850 | − | 6.42331i | 0.149785 | − | 0.259435i | −0.781363 | − | 0.624077i | \(-0.785475\pi\) |
0.931148 | + | 0.364642i | \(0.118809\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.26927 | −0.0511821 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.4373 | + | 26.7381i | 0.621480 | + | 1.07644i | 0.989210 | + | 0.146503i | \(0.0468018\pi\) |
−0.367730 | + | 0.929933i | \(0.619865\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.45751 | −0.339936 | −0.169968 | − | 0.985450i | \(-0.554366\pi\) | ||||
−0.169968 | + | 0.985450i | \(0.554366\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.17712 | − | 3.77089i | −0.0873650 | − | 0.151321i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.14575 | − | 7.18065i | 0.165830 | − | 0.287226i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −32.5203 | − | 42.5790i | −1.29873 | − | 1.70044i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.4059 | − | 21.4876i | −0.493870 | − | 0.855408i | 0.506105 | − | 0.862472i | \(-0.331085\pi\) |
−0.999975 | + | 0.00706354i | \(0.997752\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17.5830 | + | 30.4547i | 0.698862 | + | 1.21046i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 21.8745 | 0.868063 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.29150 | + | 10.8972i | 0.249278 | + | 0.431763i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.8340 | 0.428586 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.43725 | + | 11.1497i | −0.254256 | + | 0.440385i | −0.964693 | − | 0.263376i | \(-0.915164\pi\) |
0.710437 | + | 0.703761i | \(0.248497\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.26013 | − | 5.64671i | 0.128567 | − | 0.222685i | −0.794555 | − | 0.607193i | \(-0.792296\pi\) |
0.923122 | + | 0.384508i | \(0.125629\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 49.1660 | 1.93591 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.4575 | 0.882896 | 0.441448 | − | 0.897287i | \(-0.354465\pi\) | ||||
0.441448 | + | 0.897287i | \(0.354465\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −18.4373 | + | 31.9343i | −0.723726 | + | 1.25353i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 27.2288 | − | 47.1616i | 1.06718 | − | 1.84841i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24.0000 | −0.939193 | −0.469596 | − | 0.882881i | \(-0.655601\pi\) | ||||
−0.469596 | + | 0.882881i | \(0.655601\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.59412 | − | 2.76110i | −0.0622874 | − | 0.107885i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.83399 | 0.266619 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.29150 | + | 16.0934i | 0.361946 | + | 0.626908i | 0.988281 | − | 0.152646i | \(-0.0487793\pi\) |
−0.626335 | + | 0.779554i | \(0.715446\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.11438 | + | 14.0545i | 0.315613 | + | 0.546657i | 0.979568 | − | 0.201115i | \(-0.0644566\pi\) |
−0.663955 | + | 0.747773i | \(0.731123\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −15.8745 | − | 20.7846i | −0.615587 | − | 0.805993i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.35425 | − | 2.34563i | 0.0524367 | − | 0.0908231i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −24.8856 | − | 43.1032i | −0.962134 | − | 1.66646i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.17712 | − | 3.77089i | −0.0840470 | − | 0.145574i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.8745 | −0.534823 | −0.267411 | − | 0.963582i | \(-0.586168\pi\) | ||||
−0.267411 | + | 0.963582i | \(0.586168\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.03137 | + | 5.25049i | 0.116678 | + | 0.202092i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.4170 | 0.438791 | 0.219395 | − | 0.975636i | \(-0.429592\pi\) | ||||
0.219395 | + | 0.975636i | \(0.429592\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.76013 | + | 11.7089i | −0.259430 | + | 0.449346i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.72876 | − | 16.8507i | 0.372807 | − | 0.645720i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.41699 | −0.207276 | −0.103638 | − | 0.994615i | \(-0.533048\pi\) | ||||
−0.103638 | + | 0.994615i | \(0.533048\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 25.6458 | 0.979874 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26.4575 | − | 45.8258i | 1.00942 | − | 1.74836i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.5830 | − | 21.7944i | 0.479374 | − | 0.830301i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.58301 | 0.0982622 | 0.0491311 | − | 0.998792i | \(-0.484355\pi\) | ||||
0.0491311 | + | 0.998792i | \(0.484355\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −33.8745 | − | 58.6724i | −1.28679 | − | 2.22878i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 30.6863 | 1.16400 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −24.9686 | − | 43.2469i | −0.944400 | − | 1.63575i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.17712 | − | 8.96704i | 0.195537 | − | 0.338681i | −0.751539 | − | 0.659688i | \(-0.770688\pi\) |
0.947077 | + | 0.321008i | \(0.104022\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.594119 | + | 1.42526i | −0.0224076 | + | 0.0537548i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.47974 | − | 16.4194i | 0.357028 | − | 0.618390i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 24.8745 | + | 43.0839i | 0.935502 | + | 1.62034i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.82288 | + | 3.15731i | 0.0684595 | + | 0.118575i | 0.898223 | − | 0.439539i | \(-0.144858\pi\) |
−0.829764 | + | 0.558115i | \(0.811525\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 16.0000 | 0.600047 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.64575 | − | 8.04668i | −0.173985 | − | 0.301350i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.2915 | 0.571870 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −15.8745 | + | 27.4955i | −0.592844 | + | 1.02684i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.35425 | − | 2.34563i | 0.0505050 | − | 0.0874771i | −0.839668 | − | 0.543100i | \(-0.817250\pi\) |
0.890173 | + | 0.455623i | \(0.150584\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −48.4575 | −1.80465 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −20.0627 | −0.746142 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.88562 | + | 3.26599i | −0.0700302 | + | 0.121296i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.708497 | − | 1.22715i | 0.0262767 | − | 0.0455126i | −0.852588 | − | 0.522584i | \(-0.824968\pi\) |
0.878865 | + | 0.477071i | \(0.158302\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −41.0000 | −1.51852 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.1033 | 0.594788 | 0.297394 | − | 0.954755i | \(-0.403883\pi\) | ||||
0.297394 | + | 0.954755i | \(0.403883\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −13.6974 | − | 23.7246i | −0.505236 | − | 0.875094i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.50000 | + | 2.59808i | 0.0552532 | + | 0.0957014i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.9059 | − | 29.2818i | 0.621893 | − | 1.07715i | −0.367240 | − | 0.930126i | \(-0.619697\pi\) |
0.989133 | − | 0.147024i | \(-0.0469694\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.87451 | + | 21.2895i | −0.326013 | + | 0.782090i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23.7601 | + | 41.1538i | −0.871675 | + | 1.50978i | −0.0114112 | + | 0.999935i | \(0.503632\pi\) |
−0.860263 | + | 0.509850i | \(0.829701\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.00000 | + | 15.5885i | 0.329734 | + | 0.571117i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15.8745 | − | 27.4955i | −0.580818 | − | 1.00601i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −55.7490 | −2.03702 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.93725 | − | 6.81952i | −0.143672 | − | 0.248848i | 0.785204 | − | 0.619237i | \(-0.212558\pi\) |
−0.928877 | + | 0.370389i | \(0.879225\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 77.3320 | 2.81814 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.6458 | − | 18.4390i | 0.387439 | − | 0.671063i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.29150 | + | 3.96900i | −0.0832861 | + | 0.144256i | −0.904660 | − | 0.426135i | \(-0.859875\pi\) |
0.821374 | + | 0.570391i | \(0.193208\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −20.2288 | −0.734257 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.8745 | 1.55420 | 0.777100 | − | 0.629377i | \(-0.216690\pi\) | ||||
0.777100 | + | 0.629377i | \(0.216690\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −26.5830 | + | 46.0431i | −0.962369 | + | 1.66687i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.8745 | 0.573195 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.6458 | − | 30.5633i | −0.636322 | − | 1.10214i | −0.986233 | − | 0.165359i | \(-0.947122\pi\) |
0.349911 | − | 0.936783i | \(-0.386212\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 32.5203 | 1.17119 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.46863 | − | 4.27579i | −0.0887903 | − | 0.153789i | 0.818210 | − | 0.574920i | \(-0.194967\pi\) |
−0.907000 | + | 0.421130i | \(0.861633\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.46863 | + | 11.2040i | 0.232360 | + | 0.402459i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.70850 | + | 2.95920i | −0.0612920 | + | 0.106161i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.771243 | − | 1.00979i | −0.0276327 | − | 0.0361796i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.29150 | − | 10.8972i | 0.225128 | − | 0.389933i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.17712 | + | 3.77089i | 0.0778041 | + | 0.134761i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.70850 | − | 15.0836i | −0.310820 | − | 0.538355i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −42.5203 | −1.51568 | −0.757842 | − | 0.652438i | \(-0.773746\pi\) | ||||
−0.757842 | + | 0.652438i | \(0.773746\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14.4686 | − | 25.0604i | −0.515097 | − | 0.892174i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 56.8118 | 2.01999 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.937254 | + | 1.62337i | −0.0332829 | + | 0.0576476i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −27.3948 | + | 47.4491i | −0.971592 | + | 1.68285i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 44.8118 | 1.58731 | 0.793657 | − | 0.608365i | \(-0.208174\pi\) | ||||
0.793657 | + | 0.608365i | \(0.208174\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.96863 | − | 6.87386i | 0.140050 | − | 0.242573i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.87451 | −0.348031 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.00000 | −0.316423 | −0.158212 | − | 0.987405i | \(-0.550573\pi\) | ||||
−0.158212 | + | 0.987405i | \(0.550573\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.6458 | + | 27.0992i | 0.549397 | + | 0.951583i | 0.998316 | + | 0.0580106i | \(0.0184757\pi\) |
−0.448919 | + | 0.893572i | \(0.648191\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.3431 | + | 28.3071i | 0.573179 | + | 0.992775i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.23987 | + | 5.61162i | −0.113488 | + | 0.196566i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29.8745 | + | 39.1149i | 1.04518 | + | 1.36846i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −14.5830 | + | 25.2585i | −0.509571 | + | 0.882604i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.00000 | − | 5.19615i | −0.104701 | − | 0.181347i | 0.808915 | − | 0.587925i | \(-0.200055\pi\) |
−0.913616 | + | 0.406578i | \(0.866722\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.9373 | − | 27.6041i | −0.555538 | − | 0.962220i | −0.997861 | − | 0.0653641i | \(-0.979179\pi\) |
0.442324 | − | 0.896855i | \(-0.354154\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 28.1660 | 0.980615 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.3229 | + | 45.5926i | 0.915336 | + | 1.58541i | 0.806408 | + | 0.591359i | \(0.201408\pi\) |
0.108928 | + | 0.994050i | \(0.465258\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.1660 | 0.596200 | 0.298100 | − | 0.954535i | \(-0.403647\pi\) | ||||
0.298100 | + | 0.954535i | \(0.403647\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −36.4059 | + | 63.0568i | −1.26291 | + | 2.18742i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.7490 | 0.683443 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 14.9373 | 0.516307 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.7601 | + | 35.9576i | −0.716719 | + | 1.24139i | 0.245573 | + | 0.969378i | \(0.421024\pi\) |
−0.962293 | + | 0.272016i | \(0.912310\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.1458 | − | 22.7691i | 0.453302 | − | 0.785142i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 67.3542 | 2.31980 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.40588 | + | 12.8274i | 0.254770 | + | 0.441275i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −38.5830 | −1.32573 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −40.5405 | − | 70.2182i | −1.39135 | − | 2.40988i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.291503 | + | 0.504897i | 0.00999258 | + | 0.0173077i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.29150 | − | 7.43310i | 0.146938 | − | 0.254505i | −0.783156 | − | 0.621825i | \(-0.786391\pi\) |
0.930094 | + | 0.367321i | \(0.119725\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11.0405 | − | 26.4857i | 0.377578 | − | 0.905790i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.5000 | + | 18.1865i | −0.358673 | + | 0.621240i | −0.987739 | − | 0.156112i | \(-0.950104\pi\) |
0.629066 | + | 0.777352i | \(0.283437\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.61438 | − | 11.4564i | −0.225680 | − | 0.390889i | 0.730843 | − | 0.682545i | \(-0.239127\pi\) |
−0.956523 | + | 0.291656i | \(0.905794\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.40588 | − | 2.43506i | −0.0479123 | − | 0.0829865i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31.0627 | 1.05739 | 0.528694 | − | 0.848812i | \(-0.322682\pi\) | ||||
0.528694 | + | 0.848812i | \(0.322682\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.93725 | − | 8.55157i | −0.167872 | − | 0.290762i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −44.9778 | −1.52753 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.29150 | − | 16.0934i | 0.315193 | − | 0.545930i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.645751 | − | 1.11847i | 0.0218804 | − | 0.0378980i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14.8340 | −0.502054 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 43.7490 | 1.47899 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.8229 | + | 36.0663i | −0.703139 | + | 1.21787i | 0.264221 | + | 0.964462i | \(0.414885\pi\) |
−0.967359 | + | 0.253409i | \(0.918448\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 38.2804 | − | 66.3036i | 1.29117 | − | 2.23636i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36.8745 | −1.24233 | −0.621167 | − | 0.783678i | \(-0.713341\pi\) | ||||
−0.621167 | + | 0.783678i | \(0.713341\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.1974 | + | 24.5906i | 0.477780 | + | 0.827539i | 0.999676 | − | 0.0254701i | \(-0.00810828\pi\) |
−0.521896 | + | 0.853009i | \(0.674775\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −34.5608 | −1.16175 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.70850 | − | 15.0836i | −0.292403 | − | 0.506456i | 0.681975 | − | 0.731376i | \(-0.261121\pi\) |
−0.974377 | + | 0.224919i | \(0.927788\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24.2288 | + | 41.9654i | 0.812606 | + | 1.40748i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11.6144 | + | 20.1167i | −0.389096 | + | 0.673935i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18.8229 | − | 2.43506i | 0.629884 | − | 0.0814861i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.34313 | + | 5.79048i | −0.111749 | + | 0.193554i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.35425 | + | 7.54178i | 0.145384 | + | 0.251813i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.64575 | + | 8.04668i | 0.154944 | + | 0.268372i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 54.4575 | + | 94.3232i | 1.81223 | + | 3.13888i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −36.5830 | −1.21606 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.9686 | + | 34.5867i | −0.663047 | + | 1.14843i | 0.316763 | + | 0.948505i | \(0.397404\pi\) |
−0.979811 | + | 0.199927i | \(0.935929\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −27.2915 | + | 47.2703i | −0.905202 | + | 1.56786i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.9373 | −0.561156 | −0.280578 | − | 0.959831i | \(-0.590526\pi\) | ||||
−0.280578 | + | 0.959831i | \(0.590526\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −36.8745 | −1.22037 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.04052 | − | 3.53428i | 0.0674575 | − | 0.116840i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.53137 | − | 6.11652i | 0.116616 | − | 0.201985i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.8745 | 0.655600 | 0.327800 | − | 0.944747i | \(-0.393693\pi\) | ||||
0.327800 | + | 0.944747i | \(0.393693\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.854249 | − | 1.47960i | −0.0281485 | − | 0.0487545i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.41699 | −0.178303 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.405881 | − | 0.703006i | −0.0133453 | − | 0.0231147i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −26.5830 | − | 46.0431i | −0.873100 | − | 1.51225i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.79150 | − | 8.29913i | 0.157204 | − | 0.272285i | −0.776655 | − | 0.629926i | \(-0.783085\pi\) |
0.933859 | + | 0.357640i | \(0.116419\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.5516 | − | 25.3128i | 0.345816 | − | 0.829595i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18.0516 | − | 31.2663i | 0.590984 | − | 1.02361i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.56275 | − | 6.17086i | −0.116390 | − | 0.201593i | 0.801945 | − | 0.597398i | \(-0.203799\pi\) |
−0.918334 | + | 0.395805i | \(0.870466\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 23.4797 | 0.766232 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.41699 | + | 14.5787i | 0.274386 | + | 0.475251i | 0.969980 | − | 0.243184i | \(-0.0781920\pi\) |
−0.695594 | + | 0.718435i | \(0.744859\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.479741 | −0.0156225 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.93725 | − | 13.7477i | 0.258199 | − | 0.447214i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.87451 | − | 6.71084i | 0.125905 | − | 0.218073i | −0.796182 | − | 0.605058i | \(-0.793150\pi\) |
0.922086 | + | 0.386985i | \(0.126483\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.41699 | −0.110920 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.8745 | 0.514766 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.72876 | − | 11.6545i | 0.217966 | − | 0.377528i | −0.736220 | − | 0.676742i | \(-0.763391\pi\) |
0.954186 | + | 0.299214i | \(0.0967245\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.41699 | − | 9.38251i | 0.175290 | − | 0.303611i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20.2288 | 0.653903 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 28.4059 | + | 49.2004i | 0.917274 | + | 1.58876i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.874508 | 0.0282099 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −30.5830 | − | 52.9713i | −0.985524 | − | 1.70698i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.0000 | − | 20.7846i | −0.386294 | − | 0.669080i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.64575 | + | 11.5108i | −0.213713 | + | 0.370162i | −0.952874 | − | 0.303367i | \(-0.901889\pi\) |
0.739161 | + | 0.673529i | \(0.235222\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.1974 | − | 47.1073i | 0.872806 | − | 1.51174i | 0.0137234 | − | 0.999906i | \(-0.495632\pi\) |
0.859082 | − | 0.511838i | \(-0.171035\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 33.9889 | + | 58.8705i | 1.08963 | + | 1.88730i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.06275 | − | 10.5010i | −0.194163 | − | 0.336301i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.45751 | −0.238587 | −0.119293 | − | 0.992859i | \(-0.538063\pi\) | ||||
−0.119293 | + | 0.992859i | \(0.538063\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −58.3320 | −1.86240 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.8745 | − | 27.4955i | 0.506318 | − | 0.876969i | −0.493655 | − | 0.869658i | \(-0.664339\pi\) |
0.999973 | − | 0.00731102i | \(-0.00232719\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.29150 | + | 10.8972i | −0.200464 | + | 0.347214i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 42.0000 | 1.33687 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.5830 | 0.590905 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.41699 | + | 2.45431i | −0.0450123 | + | 0.0779636i | −0.887654 | − | 0.460511i | \(-0.847666\pi\) |
0.842641 | + | 0.538475i | \(0.180999\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −26.2085 | + | 45.3944i | −0.831702 | + | 1.44055i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 32.7085 | 1.03693 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.11438 | + | 14.0545i | 0.256985 | + | 0.445111i | 0.965433 | − | 0.260652i | \(-0.0839376\pi\) |
−0.708448 | + | 0.705763i | \(0.750604\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.937254 | −0.0296534 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))